Functional mixture regression

Yao, Fang; Fu, Yuejiao; Lee, Thomas C.

doi:10.1093/biostatistics/kxq067

Cited by 31 publications

(38 citation statements)

References 21 publications

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“…The goal is to estimate θ, a and b(t) based on the sample. Model (1.2) is also related to the functional mixture regression (FMR) of Yao, Fu, and Lee (2011), which is an extension of classical finite mixture regression models (DeSarbo and Cron, 1988). However, they are different, since the group label for each observation of FMR is unknown, while it is known in (1.2).…”

Section: X(t)b(t) Dtmentioning

confidence: 99%

“…We also compare the proposed method with the FMR method (Yao, Fu, and Lee, 2011) under the current simulation setting, where the number of groups is 2 for FMR. Because FMR is a nonparametric model, we can only compare the performance of the estimators of b(t).…”

Section: Estimationmentioning

confidence: 99%

“…Because FMR is a nonparametric model, we can only compare the performance of the estimators of b(t). Let b FMR (t) be the FMR estimator of b(t) proposed by Yao, Fu, and Lee (2011). The MISE and associated standard deviation of b FMR (t) are displayed in Table 2.…”

Section: Estimationmentioning

confidence: 99%

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Two-sample Functional Linear Models

Xu¹,

Zhang²,

Liang³

2019

STAT SINICA

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In this paper we study two-sample functional linear regression with a scaling transformation of regression functions. We consider estimation of the intercept, the slope function and the scalar parameter based on the functional principal component analysis. We also establish the rates of convergence for the estimator of the slope function, which is shown to be optimal in a minimax sense under certain smoothness assumptions. We further investigate semiparametric efficiency for the estimation of the scalar parameter and hypothesis testing. We also extend the proposed method to sparsely and irregularly sampled functional data and establish the consistency for the estimators of the scalar and the slope function. We evaluate numerical performance of the proposed methods through simulation studies and illustrate their utility via analysis of an AIDS data set.

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Section: X(t)b(t) Dtmentioning

confidence: 99%

Section: Estimationmentioning

confidence: 99%

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Two-sample Functional Linear Models

Xu¹,

Zhang²,

Liang³

2019

STAT SINICA

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“…This is the model considered by Yao et al. (), who represent the predictors in terms of their functional principal components and apply a multivariate mixture regression model fitting technique. Ciarleglio and Ogden () consider sparse mixture regression in the wavelet domain.…”

Section: Generalisations and Extensionsmentioning

confidence: 99%

“…A data set may be divided into latent classes, such that each class has a different regression relationship of the form (1). This is the model considered by Yao et al (2011), who represent the predictors in terms of their functional principal components and apply a multivariate mixture regression model fitting technique. Ciarleglio & Ogden (2016) consider sparse mixture regression in the wavelet domain.…”

Section: Mixture Regressionmentioning

confidence: 99%

Methods for Scalar‐on‐Function Regression

Reiss

Goldsmith

Shang

et al. 2016

Int Statistical Rev

151

109

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Recent years have seen an explosion of activity in the field of functional data analysis (FDA), in which curves, spectra, images, etc. are considered as basic functional data units. A central problem in FDA is how to fit regression models with scalar responses and functional data points as predictors. We review some of the main approaches to this problem, categorizing the basic model types as linear, nonlinear and nonparametric. We discuss publicly available software packages, and illustrate some of the procedures by application to a functional magnetic resonance imaging dataset.

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Cluster analysis with regression of non‐Gaussian functional data on covariates

et al. 2021

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Cluster analysis with functional data often imposes normality assumptions on outcomes and is typically carried out without covariates or supervision. However, nonnormal functional data are frequently encountered in practice, and unsupervised learning, without directly tying covariates to clusters, often makes the resulting clusters less interpretable. To address these issues, we propose a new semiparametric transformation functional regression model, which enables us to cluster nonnormal functional data in the presence of covariates. Our model incorporates several unique features. First, it omits the normality assumptions on the functional response, which adds more flexibility to the modelling. Second, our model allows clusters to have distinct relationships between functional responses and covariates, and thus makes the clusters formed more interpretable. Third, unlike various competing methods, we allow the number of clusters to be unspecified and data-driven. We develop a new method, which combines penalized likelihood and estimating equations, to estimate the number of clusters, regression parameters, and transformation functions simultaneously; we also establish the large-sample properties such as consistency and asymptotic normality. Simulations confirm the utility of our proposed approach. We use our proposed method to analyze Chinese housing market data and garner some interesting findings.

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Functional mixture regression

Cited by 31 publications

References 21 publications

Two-sample Functional Linear Models

Two-sample Functional Linear Models

Methods for Scalar‐on‐Function Regression

Cluster analysis with regression of non‐Gaussian functional data on covariates

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